When cloning a large chest, the right half is cloned as a small chest on the left and the double chest is cloned either in the same block or one block to the right.

Steps to reproduce:
1. Place a double chest facing west.
2. Place two distinct items in left and right sides of chest.
3. Use /tp to determine coordinates of chest.
4. Use /clone to clone the chest two blocks to the east.
5. Observe overlapping small and large chests at destination.
6. Observe small chest on left contains item placed in right side of original chest, large cloned chest contains both items from original chest.

This result was observed while trying to reproduce the clone error shown in the "Alternate result" screenshot, where the large chest overlapped the block to its right (a hopper which was also cloned). I don't know what the condition is that changes the result, but both results likely have the same cause.